Uniform approximations of the fundamental solution of the equation of internal waves. (English. Russian original) Zbl 0894.76015
J. Appl. Math. Mech. 60, No. 3, 439-447 (1996); translation from Prikl. Mat. Mekh. 60, No. 3, 443-450 (1996).
Summary: New representations of the fundamental solution of the equation of internal waves as convergent and asymptotic series are proposed using special functions. A system of three formulae is constructed, each defining a uniform approximation of the fundamental solution in some space-time domain, the union of these domains covering the whole space-time continuum. The results of a numerical experiment are presented, which show that the relative approximation error does not exceed \(0.5\%\), while the computer time required to calculate the fundamental solution is reduced by a factor of over 200 as compared to the exact formulae.
References:
| [1] | Gabov, S. A.; Sveshnikov, A. G., Linear Problems of the Theory of Unsteady Internal Waves (1990), Nauka: Nauka Moscow · Zbl 0713.76003 |
| [2] | Voison, B., Internal wave generation in uniformly stratified fluids, Part 1, Green’s function and point sources, J. Fluid Mech., 231, 439-480 (1991) · Zbl 0850.76809 |
| [3] | (Abramowitz, M.; Stegun, I. A., Handbook of Mathematical Functions and Fomudas, Graphs, and Mathematical Tables (1964), Wiley-Interscience: Wiley-Interscience New York) · Zbl 0171.38503 |
| [4] | Fedoryuk, M. V., The Saddle point Method, (1977), Nauka: Nauka Moscow · Zbl 0463.41020 |
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